Optimal. Leaf size=13 \[ \frac {e^x}{x^2 \log \left (\frac {1}{x}\right )} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.28, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^x+e^x (-2+x) \log \left (\frac {1}{x}\right )}{x^3 \log ^2\left (\frac {1}{x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^x}{x^3 \log ^2\left (\frac {1}{x}\right )}-\frac {2 e^x}{x^3 \log \left (\frac {1}{x}\right )}+\frac {e^x}{x^2 \log \left (\frac {1}{x}\right )}\right ) \, dx\\ &=-\left (2 \int \frac {e^x}{x^3 \log \left (\frac {1}{x}\right )} \, dx\right )+\int \frac {e^x}{x^3 \log ^2\left (\frac {1}{x}\right )} \, dx+\int \frac {e^x}{x^2 \log \left (\frac {1}{x}\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 13, normalized size = 1.00 \begin {gather*} \frac {e^x}{x^2 \log \left (\frac {1}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.22, size = 12, normalized size = 0.92
method | result | size |
risch | \(-\frac {{\mathrm e}^{x}}{\ln \left (x \right ) x^{2}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 11, normalized size = 0.85 \begin {gather*} -\frac {e^{x}}{x^{2} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 12, normalized size = 0.92 \begin {gather*} \frac {e^{x}}{x^{2} \log \left (\frac {1}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 10, normalized size = 0.77 \begin {gather*} \frac {e^{x}}{x^{2} \log {\left (\frac {1}{x} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 11, normalized size = 0.85 \begin {gather*} -\frac {e^{x}}{x^{2} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.96, size = 12, normalized size = 0.92 \begin {gather*} \frac {{\mathrm {e}}^x}{x^2\,\ln \left (\frac {1}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________